If x is obtuse and sin x equals b how do you show sin 2x is less than b?

Answer 1

you need to explain it better but with what i got i if sin x equals b obviously sin 2x is double of b hence sin 2x is more than b. {Not obvious at all, actually. And the above is false. Sin(Pi/2) = 1 and Sin(Pi)=0. But clearly 2 is not greater than 0. Contradiction.}

Obtuse means Pi/2 < x < Pi

So, sin(x) = b means b>0, because sin(y) > 0 if 0<y<Pi

sin(2x)=2sin(x)cos(x)

cos(x) < 0 because cos(Pi/2)= 0 and the derivative is negative there.

Hence, sin(2x) = 2 sin(x) cos(x) = 2*b*(-K), where K is a positive constant

Since b>0, -2Kb < b